From its inception, broadcast frequency modulation transmissions, such the type presently occupying the 88-108 Mhz range have been favored for their highly noise resistant characteristics and extended frequency range.
The extended frequency range of these systems is provided due to the fact that the bandwidth allowed an FM broadcast station is extremely wide, as compared, for example, to conventional amplitude modulation (AM) broadcast stations such as those which operate in the various frequency bands below 30 Megahertz. However, the bandwidth of a frequency modulation (FM) transmission is several times that of even an AM station carrying similar frequency content information. While, in theory, it is possible to limit FM modulation to the point where its bandwidth is similar to that of an FM station, such limitation on the modulation index .beta. effectively removes the noise resistance of F.M. transmissions.
In particular, let us consider the case of a simple frequency-modulated signal which may be written as: EQU f.sub.c (t)=cos w.sub.c t cos (.beta.sin w.sub.m t)-sin w.sub.c t sin (.beta.sin w.sub.m t),
which f.sub.c (t) is the frequency-modulated carrier, w.sub.c is the carrier frequency of that carrier, w.sub.n is the modulating frequency of a single sinusoidal signal carried by said carrier, t is time and .beta. is defined as: EQU .beta.=.DELTA.w/w.sub.n,
where
.DELTA.w is the maximum frequency deviation of the FM signal in radians.
Classically, broadcast engineers have tended to think of bandwith in terms of the highest frequency being carried by the carrier. The origin of this approach resides mainly in the consideration of FM amplitude modulated signals. Here, the bandwidth of the signal is absolutely limited to twice the highest frequency carried by the carrier. As noted above, in the case of FM transmissions, the particular magnitude of the limitations is largely dependent upon the amplitude of the modulation index .beta.. Increased modulation index results in multiplying the narrowband bandwith of the signal which is substantially equal to twice the highest frequency carried by the carrier by a number n corresponding to the number of significant sidebands. As the modulation index .beta. and the number of sidebands are increased, the result is a signal which has significant redundancy and, accordingly, as compared to AM, also has significant immunity to noise in the environment where the signal is being received.
As compared to AM, where the signal-to-noise ratio of the input radio frequency signal equals the signal to noise ratio of the demodulated signal, assuming the perfect demodulator, demodulated FM signals with high modulation indices have significantly higher signal-to-noise ratios compared to the input radio frequency FM signal. The gain of signal-to-noise ratio increases as the .beta. of the signal increases. Likewise, the number of significant sidebands also increases from one pair of sidebands where, for example, .beta. equals 0.2. A number of significant sidebands may be calculated by reference to the Bessel functions. For example, in the case of .beta.=0.2, the zero order Bessel function has a value of 0.99 and the first order function has a value of 0.1. On the other hand, if we increase the .beta. of the signal to 2.0, we find that the zero order Bessel function has an amplitude of 0.22, the first order Bessel function has an amplitude of 0.58, the second order Bessel function has an amplitude of 0.35, the third order Bessel function has an amplitude of 0.13, and the fourth order Bessel function has an amplitude of 0.03, telling us that there are four significant pairs of sidebands.
If we go back to the consideration of bandwidth as a function of the highest frequency being modulated, the existence of four significant sidebands, at modulation index .beta.=2.0, we see that the bandwidth of the signal will be equal to eight times the highest modulating frequency or four times the bandwidth of a similar AM signal.
When we consider that the Federal Communications Commission has set a maximum bandwidth of about 150 kilohertz for an FM signal and take into account that 15 kilohertz is the highest audio frequency typically transmitted by a commercial FM station, it can be seen that a maximum .beta. of four can be tolerated for such relatively high frequencies.
On the other hand, if we consider the possibility of filtering the signal to be transmitted, and consider that most of the energy is at the lowest frequencies, significantly higher modulation indexes can be tolerated for these frequencies while still retaining high fidelity in the transmitted signal.
In the case of stereo transmission, this problem is somewhat more complicated, but the same principles are applied. More particularly, in the place of stereo transmission, the signal which is impressed by frequency modulation onto the FM carrier in the FM broadcast band is the composite of an audio signal varying between 50 and 15,000 kHz, a 19 kilohertz pilot and a double sideband suppressed carrier signal centered at 38 kilohertz and extending between approximately 23 kilohertz and 53 kilohertz. The first audio signal ranging from 50 to 15,000 kilohertz is comprised of the sum of the left and right channels and, in the case of a simple FM receiver, is the only signal which is detected. This may be referred to as the baseband signal. The second, double sideband signal, ranging from 23 to 52 kilohertz is effectively an AM double sideband signal with a suppressed carrier of 38 kilohertz and comprises the difference between the left and right signals. This may be referred to as the stereo information signal.
Typically, the stereo information signal is generated using the 19 kilohertz pilot as the synchronization source for demodulation. The left channel signal is obtained by adding the composite signal to the stereo information signal, and the right channel is obtained by subtracting the stereo information signal from the composite signal.
As can be seen from the above, the successful operation of the system depends upon a relatively flat, wide band filter system for receiving the composite signal and the stereo information signal. Typically, this is done by using a tuning circuit which comprises a plurality of tuning networks whose peaks are staggered in order to synthesize a flat response across the bandpass with relatively sharp skirts. This approach is substantially the equivalent of similar filtering techniques used in AM broadcast reception in order to pass relatively narrow band signals while excluding adjacent stations.
While initially it would appear that the above signal would substantially fill the information carrying capability of the broadcast FM signal, in point of fact, even higher frequency signals may be carried by the FM carrier without interfering with operation of the standard FM broadcast receiver. In particular, this is typically done by adding two possible additional signals. The first of these is an FM signal having a carrier of 67 kilohertz and a bandwith of approximately 6 kilohertz. This narrow bandwidth signal is referred to as a subcarrier transmission and the demodulated output is sometimes called an SCA signal.
A second narrow band FM signal may also be transmitted at a subcarrier frequency of 92 kilohertz and also with a bandwidth of approximately 6 kilohertz.
In accordance with the prior art, reception of the subcarrier FM signals demands good filtering of these signals from each other and from adjacent composite and stereo information signals. This is done in the conventional manner using a cascade of tuned ferrite transformers, each of which is tuned in such a manner as to create effective rejection of signals outside the passband and a relatively flat response within the passband.
In particular, tuning is provided in prior art systems using a plurality of tuned transformers comprising a variable inductance and a fixed capacitance with the transformers being coupled to each other via relatively large coupling capacitors which couple the output of one transformer to the other for further filtering.
However, these tuned ferrite transformers are relatively expensive items and the necessity of having four to receive one subcarrier channel and eight to receive two subcarrier channels represents a significant part of the cost of an FM subcarrier receiver.